Mathematical Modeling

Name: Mathematical Modeling
ISBN: 9787115504975

陈雄达 / 梁进 / 钱志坚 / 亦挺Posts & Telecom Press · ChinaJul 2019

4.0

Word count: 110K words
Chapters: 40
ISBN: 9787115504975

Report an error Find this book

Summary

Building on conventional mathematical modeling instruction, this book strengthens the analytical and computational components, illustrates in-depth applications of each model through examples, and notably adds coverage of data processing models to meet modeling needs in the big data era. The book comprises five chapters: discrete models, probability and statistics models, dynamic models, optimization models, and competition strategies. The four model categories address most modeling problems, while the competition strategies chapter introduces the basics of competitions and analyzes and comments on first-prize papers from the Tongji University Mathematical Modeling Competition, offering guidance to students interested in participating.

Editor's review

Mathematical Modeling by Professor Chen Xiongda is a classic textbook for science and engineering students at higher education institutions, whose core value lies in building a solid bridge between abstract mathematical theory and complex real-world problems. Rather than merely listing theories, the book uses carefully selected cases—such as population growth models, infectious disease transmission models, and optimization problems—to systematically demonstrate the full process of distilling practical problems into mathematical models and solving and analyzing them with mathematical tools. The author particularly emphasizes model assumptions, scope of applicability, and limitations—a rigorous mindset that distinguishes this book from similar textbooks. For beginners, the step-by-step structure helps overcome apprehension about mathematical modeling; for learners with some foundation, the discussion of model refinement and extension offers new inspiration. Overall, this is an excellent work that emphasizes methodology and practice and effectively cultivates readers' ability to use mathematics to solve practical problems.

Who it's for

A good fit for

Undergraduate or graduate students in mathematics, computer science, engineering, and related fields
Students preparing for the CUMCM and other academic competitions
Self-learners interested in using mathematical tools to analyze real social, economic, or scientific problems
Researchers or engineers seeking to supplement their knowledge of mathematical modeling and case studies

Not a good fit for

Readers interested only in pure mathematical theory and not in applications
Readers seeking quick mastery of software操作 rather than modeling ideas and processes

Reading tips

Read in chapter order, focusing on the logical chain from problem statement to model construction in each case
Practice actively by independently completing or adapting the examples and exercises to consolidate understanding
Apply the methods to current social or technological issues through simple modeling exercises to learn by doing

About the publisher

Posts & Telecom Press China · Founded in 1953

Posts & Telecom Press is known for its strengths in science and technology, computing, and information and communications titles, and has extended its publishing into photography, art, software learning, and inspirational growth, giving it a fairly diverse range. Its catalog includes computing and communications works such as Refactoring and Patterns (Revised Edition) and Huawei Switch Learning Guide (Second Edition), alongside bilingual collector's editions such as The Little Prince (Chinese-English-French illustrated collector's edition), The Great Gatsby, and Three Days to See. Beijing Ten Years: 1980-1990 and Ghost Blade: WLOP Personal Illustration Collection reflect its presence in photography and art. Its authors include Antoine de Saint-Exupéry, Helen Keller, Joshua Kerievsky, Wang Da, Zhang Zhaozeng, and WLOP.

版权信息
内容提要
前言
第1章图论模型
1.1 图论模型的基本理论
1.2 图的独立集应用
1.3 竞赛图应用
1.4 Dijkstra算法应用
1.5 Kruskal算法应用
1.6 匹配算法应用
1.7 习题
第2章概率统计模型
2.1 概率统计模型的基本理论
2.2 蒙特卡洛模型应用
2.3 马尔科夫模型应用
2.4 逻辑回归模型应用
2.5 聚类分析模型应用
2.6 习题
第3章动态模型
3.1 动态模型的基本理论
3.2 简单动态模型示例
3.3 差分方程模型应用
3.4 常微分方程模型应用
3.5 常微分方程组模型应用
3.6 偏微分方程模型应用
3.7 模型参数拟合
3.8 习题
第4章优化模型
4.1 优化模型的基本理论
4.2 微积分优化方法应用
4.3 线性规划模型和整数规划模型应用
4.4 非线性规划模型应用
4.5 变分优化模型应用
4.6 一些优化计算方法介绍
4.7 习题
第5章竞赛攻略
5.1 各种数学建模竞赛简介
5.2 如何参加数学建模竞赛
5.3 数学建模竞赛题目分析及论文点评
参考文献

FAQ

Does this book require a strong mathematical background?

The book builds on advanced mathematics, linear algebra, and probability and statistics; knowledge at the lower-undergraduate level is sufficient. Core mathematical tools are briefly reviewed, with emphasis on application rather than theoretical derivation.

Does the book include programming implementations?

The book focuses on model construction, analysis, and solution approaches. Solutions are mostly presented through mathematical derivation and analytical results; tools such as MATLAB may be mentioned for numerical computation, but detailed code is not provided. Readers need to implement the computational parts themselves based on the models.

Is this book helpful for mathematical modeling competitions?

Very helpful. The model types covered (such as optimization, evaluation, and prediction) and the modeling methodology are core to mathematical modeling competitions. By studying the case approaches and writing conventions in the book, participants can systematically improve their modeling skills, paper writing, and analysis of model results.

Comments

Find this book

This site is an index: you start “Search all sources” in your browser, and the entries it lists all point to third-party sites; please judge their availability yourself.

About the author

陈雄达 Author

Public information about Chen Xiongda is currently limited, and basic details such as his life background, nationality, and dates of birth and death have not been clearly recorded. Within the library, he is associated with only one work, Mathematical Modeling, which is classified under popular science. The book takes mathematical modeling as its subject and is presumably intended for readers who wish to understand how mathematical methods are applied to practical problems, covering the basic process of extracting a problem from a real-world situation, building a model, solving it, and testing the result. Based on the available material, Chen Xiongda's writing emphasizes methods and applications and serves teaching or introductory purposes, with attention to connecting abstract mathematical tools with concrete cases to lower the barrier to entry. Because related introductions are scarce, his full body of work, other writings, and academic or teaching experience remain unclear; this profile offers only a cautious overview grounded in the facts available in the library and the work's category.

梁进 Author

Public information about Liang Jin is limited, and his nationality, dates of birth and death, and academic background cannot be confirmed at present. Judging from the three works held in the library, his writing spans science popularization and architectural culture: Mathematical Modeling addresses the application of mathematical methods and reflects his attention to how mathematical tools are put into practice, while Shihua Shuxue and Who Holds Mathematics Dancing in the Sky: Interpreting the Mysteries of Ancient and Modern Architecture link mathematics with poetry and with architecture past and present, attempting to build bridges between abstract mathematical structures and concrete cultural and spatial experience. This choice of subjects shows an author who presents the beauty of mathematics in an accessible yet rigorous way, helping readers understand its usefulness and charm where the humanities and engineering meet. The books suit general readers interested in popular science and architectural culture.

钱志坚 Author

Qian Zhijian: publicly available information about this author is limited, and no clear record has been found regarding his background, nationality, or dates of birth and death. According to the library's holdings, only one work by him is included, Mathematical Modeling, commonly classified under popular science. It can therefore be inferred that Qian's writing leans toward applied mathematics and science popularization, focusing on how mathematical methods are used to abstract, simplify, and solve practical problems and presenting these ideas to readers in a relatively accessible way. The subject of mathematical modeling typically involves model assumptions, variable selection, data processing, and result verification, and places certain demands on readers' logical thinking and interdisciplinary understanding. Although information about the author himself is very scarce, this work still offers an introductory window for readers who wish to understand the basic ideas of mathematical modeling and reflects the author's attempt at science communication.

亦挺 Author

Yi Ting is an author about whom limited public information is currently available; the library holds only one work by this author, Mathematical Modeling. Judging from the title and its common classification as popular science, the book presumably centers on mathematical modeling and is intended for readers who wish to understand modeling ideas and methods. Mathematical modeling is the process of translating real-world problems into mathematical language and solving them, involving steps such as model assumptions, variable selection, solution, and verification; it is widely used in science and engineering study and in the analysis of practical problems. Yi Ting's writing in this direction serves an introductory and popularizing role, seeking to present relatively specialized content in a more readable form for general readers. Because the author's nationality, dates of birth and death, education, and personal experience cannot be confirmed, this introduction makes no speculation and offers only an objective description of the subject and positioning of the surviving work.